Schrödinger Equation Eigensystem Model Documents

Main Document

The Schrödinger Numerov Eigensystem Model solves the time-independent Schrödinger Equation with arbitrary potential energy V(x) using the Numerov method recast on a discrete lattice. As shown by Pillai, Goglio, and Walker, the resulting matrix eigenvalue problem can be solved with just a few lines of code. In this model, we demonstrate how to do this computation in Java using the linear algebra package in the Apache Commons Math library. Users can adjust the location of the hard hard walls at x-minimum and x-maximum and the potential V(x) in the region between the walls. The main window shows the potential and the energy eigenvalue spectrum along with a superimposed wave function psi. A second window shows the normalized wave function. The energy eigenvalue can be set by dragging the cursor in the main window or by entering the quantum number n.

The Schrödinger Numerov Eigensystem Model was developed using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed. You can modify this simulation if you have EJS installed by right-clicking within the map and selecting "Open Ejs Model" from the pop-up menu item.